Learning to Optimise FISTA‐PnP for Sparse Radar Imaging

This work introduces a plug‐and‐play (PnP) framework for sparse radar imaging that combines the Fast Iterative Shrinkage‐Thresholding Algorithm (FISTA) with reinforcement learning (RL)‐based parameter adaptation. Sparse radar imaging aims to reconstruct high‐resolution images from undersampled measurements, but conventional PnP pipelines rely on manual parameter tuning, and ADMM‐based solvers often converge slowly with high computational costs. To address these issues, the proposed framework leverages FISTA's momentum‐accelerated updates for faster convergence, along with an RL policy that adaptively sets the step size, denoising strength and stopping criterion. By casting parameter selection as a sequential decision‐making problem, we eliminate the need for handcrafted schedules. Extensive experiments on simulated datasets, including AIR‐SARShip maritime targets, show consistent improvements over classical parameter‐selection strategies and recent unrolled optimisation networks. At a 25% sampling ratio, the framework achieves high‐fidelity reconstructions in just 10 iterations, compared to 20–30 iterations for competing methods. Overall, the RL‐enhanced FISTA‐PnP framework provides an efficient solution for high‐quality radar image reconstruction from sparse measurements, with strong potential for real‐world applications. Preliminary tests on real RADARSAT‐1 echoes also show consistent improvements.